I have googled and found no versions with the word penis (probably on the grounds that, no what, penis' arent funny!)
However, I did find the following:
Martin Gardner
The boy stood on the burning deck,
The flames ’round him did roar;
He found a bar of Ivory Soap
And washed himself ashore.
Anon.
The boy stood on the burning deck
And wished he hadn’t been born.
His mother said he wouldn’t have been
If the johnny hadn’t torn.
Anon.
The boy stood on the burning deck,
His feet were covered in blisters.
He had no trousers of his own [or His trousers burnt right off his legs]
And so he wore his sister’s.
Only Fools and Horses
The boy stood on the burning deck
His pockets full of crackers
One slipped down his trouser-leg
And burnt off both his… kneecaps!
Colin Thompson
The boy stood on the burning duck
A stupid thing to do
Because the duck was roasting
On the barbecue.
Casabazonka
Spike Milligan
The boy stood on the burning deck
Whence all but he had fled –
The twit!
Anon.
The boy stood on the burning deck
Smoke billowing through the air
‘I can’t stand it any more!’ he cried,
And sat down on a chair
Anon.
The boy stood on the burning deck
Eating a thre’penny Walls,
Till a bit fell down his trouser leg
And paralysed his kneecap.
The boy stood on the burning deck
His lips were all a-quiver
He gave a cough, his leg fell off
And floated down the river.
The boy stood on the burning deck,
Picking his nose like mad.
He rolled it into little balls
And flicked them at his dad.
The boy stood on the burning deck
His head was in a whirl.
He put his head between his legs
And wished he was a girl. (submitted by Dave Stewart)
The following two kindly submitted by Dauvit:
The boy stood on the burning deck.
Alas, he is no more
For what he thought was H2O
Was H2S04.
The boy stood on the burning deck
Playing a game of cricket.
The ball ran up his trouser leg
And hit his middle wicket.
This one from Seyom Derf submitted October 2015
The boy stood on the burning deck,
Shouting to passing ducks.
“I wish I’d joined the RAF
This being a sailor sucks!”